A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus

Question

Represent the following situations mathematically:

A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs 750. We would like to find out the number of toys produced on that day.

Answer 1

Let the number of toys produced on that day be x.

Therefore, the cost of production (in rupees) of each toy that day = 55 – x

So, the total cost of production (in rupees) that day = x (55 – x)

Therefore, x (55 – x) = 750

i.e., 55x – x² = 750

i.e., – x² + 55x – 750 = 0

i.e., x² – 55x + 750 = 0

Therefore, the number of toys produced that day satisfies the quadratic equation

x² – 55x + 750 = 0

which is the required representation of the problem mathematically.